Thick film element having coated substrate with high heat conductivity

ABSTRACT

The present invention provides a thick film element having a coated substrate with high heat conductivity, which comprises a carrier, a thick film coating deposited on the carrier and a covering layer overlaid on the coating. The thick film coating is a heating material, and the mode of heating is electrical heating. The carrier, the thick film coating and the covering layer are selected from a material that fulfills every of the following equations: 
     
       
         
           
             
               
                 
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     wherein 10≤a≤10 4 , 0&lt;b≤10 6 , 0&lt;c≤10 3 . The coated substrate of the thick film element of the present invention has high heat conductivity and is suitable for coating products with a heated substrate. The present invention improves heat transfer efficiency and reduces heat loss when double-sided heating is not required.

FIELD OF THE INVENTION

The present invention relates to the field of thick film, and more particularly to a thick film element having a coated substrate with high heat conductivity.

BACKGROUND OF THE INVENTION

Thick film heating elements refer to heating elements that are made by fabricating exothermic materials on a substrate into thick films and providing electricity thereto to generate heat. The conventional heating methods include electrical heated tube heating and PTC heating. An electrical heated tube heating element uses a metal tube as the outer case and distributes nickel-chromium or iron-chromium alloy spirally therein to form heater strips; the clearance space is then filled with magnesite clinker that has excellent thermal conductivity and insulativity and sealed with silica gel from two ends of the tube. The PTC heating method uses ceramics as the exothermic material. Both electrical heated tube heating and PTC heating conduct heat indirectly with low thermal efficiency, and are structurally huge and bulky. Besides, in consideration of environmental protection, heaters using these two types of heating methods stain easily after repeatedly heating and cleaning thereof is not easy. Additionally, PTC heaters contain lead and other hazardous substances and are easily oxidized, causing power attenuation and short service life.

Chinese application CN201310403454.9 discloses a ceramic tile-based resistance slurry for thick film circuits and the preparation method thereof, which provides a resistance slurry that matches ceramic tiles and provides a possibility for preparation of a new underfloor heating elements. The raw materials of the resistance slurry include solid phase contents (including glass ceramic powder and silver powder) and organic binding agent, with the weight percentage of each of the materials being 70-85% of glass ceramic powder and 15-30% of organic binding agent; the sum of which are 100%. The resistance slurry is mainly used to be printed on the back of ceramic tiles to form a thick film circuit.

Chinese application CN201020622756.7 discloses a thick film circuit device, which comprises a ceramic substrate, a thick film circuit wafer and electric wires. The thick film circuit wafer is disposed on the ceramic substrate, and outer sides of the ceramic substrate are covered by an epoxy layer. The two electric wires are connected to both sides of the ceramic substrate, and the connection points between the electric wires and the ceramic substrate are covered by in the epoxy layer.

It could be seen from the above technologies that thick film technology is developing gradually; however, at present the researches mostly focus on developing resistance slurry for thick film circuits but rarely on the component products of thick films. The technical solution of the above-mentioned thick film circuit device realizes disposing thick film circuits within the ceramic substrate and epoxy layer, but thermal conductivity thereof is not excellent. The application of thick films in products greatly broadens the development of heating products. The existing heating device could meet the demands of heating; however, heating device that performs unilateral heat transfer is rarely seen, or unilateral heat transfer of such device is too poor, making it difficult to reduce heat loss by keeping high unilateral thermal conduction properties.

SUMMARY OF THE INVENTION

To solve the problems mentioned above, the present invention provides a thick film element having a coated substrate with high heat conductivity that has the advantages of small volume, high efficiency, environmental-friendly, high safety performance and long service lifespan.

The concept of thick film in the present invention is a term comparative to thin films. Thick film is a film layer with a thickness ranging from several microns to tens of microns formed by printing and sintering on a carrier; the material used to manufacture the film layer is known as thick film material, and the coating made from the thick film is called thick film coating. The thick film element has the advantages of high power density, fast heating speed, high working temperature, fast heat generating rate, high mechanical strength, small volume, easy installation, uniform heating temperature field, long lifespan, energy saving and environmental friendly, and excellent safety performance.

The thick film element having a coated substrate with high heat conductivity of the present invention comprises a carrier, a thick film coating deposited on the carrier and a covering layer overlaid on the coating. The thick film coating is a heating material, and the mode of heating is electrical heating. The carrier, the thick film coating and the covering layer are selected from a material that fulfills every of the following equations:

${{\lambda_{3}A\; \frac{T_{3} - T_{0}}{d_{3}}} = {a \times \lambda_{1}A\; \frac{T_{1} - T_{0}}{d_{1}}}},{{\lambda_{2}A\; \frac{T_{2} - T_{0}}{d_{2}}} = {b \times \lambda_{1}A\; \frac{T_{1} - T_{0}}{d_{1}}}},{{{\lambda_{2}A\; \frac{T_{2} - T_{0}}{d_{2}}} = {c \times \lambda_{3}A\; \frac{T_{3} - T_{0}}{d_{3}}}};}$ 10 ≤ a ≤ 10⁴, 0 < b ≤ 10⁶, 0 < c ≤ 10³;

T₂<T_(Minimum melting point of the covering layer); T₂<T_(Minimum melting point of the carrier);

T₀≤25° C.;

wherein the value of

$\lambda_{1}A\; \frac{T_{1} - T_{0}}{d_{1}}$

represents the heat transfer rate of the covering layer; the value of

$\lambda_{2}A\; \frac{T_{2} - T_{0}}{d_{2}}$

represents me neat generating rate of the thick film coating; the value of

$\lambda_{3}A\; \frac{T_{3} - T_{0}}{d_{3}}$

represents the heat transfer rate of the carrier; λ₁ represents the heat conductivity coefficient of the covering layer at the temperature of T₁; λ₂ represents the heat conductivity coefficient of the thick film coating at the temperature of T₂; λ₃ represents the heat conductivity coefficient of the carrier at the temperature of T₃; A represents the contact area of the thick film coating with the covering layer or the carrier; d₁ represents the thickness of the covering layer; d₂ represents the thickness of the thick film coating; d₃ represents the thickness of the carrier; T₀ represents the initial temperature of the thick film element; T₁ represents the surface temperature of the covering layer; T₂ represents the heating temperature of the thick film coating; T₃ represents the surface temperature of the carrier; d₂≤50 μm; and d₁≥10 μm; 10 μm≤d₃≤20 cm; T_(Minimum melting point of the carrier)>25° C.; λ₃≥λ₁; the covering layer refers to a dielectric layer covering the thick film coating by printing and/or sintering or gluing, and the area of the covering layer is larger than that of the thick film coating.

The carrier is the dielectric layer carrying the thick film coating. The thick film coating covers the carrier by printing, coating, spraying or sintering, and is the coated substrate of the thick film element.

The heat conductivity coefficient refers to the heat transferred by a one-meter-thick material having a temperature difference between two side surfaces of 1 degree (K, ° C.) through one square meter (1 m²) area within one second (1S) under a stable heat transfer condition. Unit of the heat conductivity coefficient is watt/meter·degree (W/(m·K), and K may be replaced by ° C.).

The covering layer, the thick film coating and the carrier stick closely with each other at the electrical heating parts of the thick film elements, and both sides of the thick film coating connect to external electrodes. When given electricity, the thick film coating is heated and becomes hot after electricity energy is transformed to thermal energy. Heat generating rate of the thick film coating could be calculated by

$\lambda_{2}A\; \frac{T_{2} - T_{0}}{d_{2}}$

according to heat conductivity coefficient, contact area, initial temperature, heating temperature and thickness of the thick film coating, wherein T₂ represents the heating temperature of the thick film.

The present invention features in that the thick film element has a coated substrate having high heat conductivity, and that the heat generating rate of the covering layer, the thick film coating and the carrier should meet the following requirements:

(1) The heat transfer rate of the covering layer and the thick film coating should satisfy the following formula:

${{\lambda_{3}A\; \frac{T_{3} - T_{0}}{d_{3}}} = {a \times \lambda_{1}A\; \frac{T_{1} - T_{0}}{d_{1}}}},$

wherein 10≤a≤10⁴; for those thick film elements satisfied the above equation, the heat transfer ability of their carrier is superior to that of the covering layer, which means that the carrier is fast while the covering layer is slow at temperature rising or that the temperature difference between the covering layer and the carrier is large after stable heat balance. Therefore, the thick film elements generally show the technical effect of carrier heating.

(2) The heat generating rate of the thick film coating and the heat transfer rate of the covering layer should satisfy the following formula:

${{\lambda_{2}A\; \frac{T_{2} - T_{0}}{d_{2}}} = {b \times \lambda_{1}A\; \frac{T_{1} - T_{0}}{d_{1}}}},$

wherein 0<b≤10⁶; if the heat generating rate of the thick film coating is much larger than the heat transfer rate of the covering layer, the continuously accumulated heat of the thick film coating could not be conducted away, such that the temperature of the thick film coating keeps rising, and when the temperature is higher than the minimum melting point of the covering layer, the covering layer would begin to melt or even burn, which would destroy the structure of the covering layer or the carrier, thus destroying the thick film elements.

(3) The heat generating rate of the thick film coating and the heat transfer rate of the carrier should satisfy the following formula:

${{\lambda_{2}A\; \frac{T_{2} - T_{0}}{d_{2}}} = {c \times \lambda_{3}A\; \frac{T_{3} - T_{0}}{d_{3}}}},{0 < c \leq 10^{3}},$

if the heat generating rate of the thick film coating is much larger than the heat transfer rate of the carrier, the continuously accumulated heat of the thick film coating could not be conducted away, such that the temperature of the thick film coating keeps rising, and when the temperature is higher than the minimum melting point of the carrier, the carrier would begin to melt or even burn, which would destroy the structure of the carrier, thus destroying the thick film elements.

(4) The heating temperature of the thick film coating could not be higher than the minimum melting point of the covering layer or the carrier, and should meet the requirements: T₂<T_(Minimum melting point of the covering layer) and T₂<T_(Minimum melting point of the carrier). Excessively high heating temperature should be avoided to prevent destruction of the thick film elements.

When the above-mentioned requirements are met, the heat transfer rate of the covering layer and the carrier is determined by properties of the material and the thick film element.

The formula for calculating the heat transfer rate of the carrier is

${\lambda_{3}A\; \frac{T_{3} - T_{0}}{d_{3}}},$

wherein λ₃ represents the heat conductivity coefficient of the carrier, with the unit being W/m·k, and is determined by properties of the materials for preparing the carrier; d₃ represents the thickness of the carrier, and is determined by preparation technique and requirements of the thick film elements; T₃ represents the surface temperature of the carrier, and is determined by properties of the thick film elements.

The formula for calculating the heat transfer rate of the covering layer is

${\lambda_{1}A\; \frac{T_{1} - T_{0}}{d_{1}}},$

wherein λ₁ represents the heat conductivity coefficient of the covering layer, with the unit being W/m·k, and is determined by properties of the material for preparing the covering layer; d₁ represents the thickness of the covering layer, and is determined by preparation technique and requirements of the thick film elements; T₁ represents the surface temperature of the covering layer, and is determined by properties of the thick film elements.

Preferably, the heat conductivity coefficient of the carrier λ₃ is ≥3 W/m·k, the heat conductivity coefficient of the covering layer λ₁ is ≤3 W/m·k; wherein 10≤a≤10⁴, 10⁴≤b≤10⁶, 10≤c≤10³.

Preferably, the carrier and the thick film coating are bound by printing or sintering; the thick film coating and the covering layer are bound by printing, coating, spraying, sintering, or gluing.

Preferably, the region between the carrier and the covering layer without the thick film coating is bound by printing, coating, spraying or sintering, or with gluing.

Preferably, the carrier includes polyimides, organic insulating materials, inorganic insulating materials, ceramics, glass ceramics, quartz, stone materials, fabrics and fiber.

Preferably, the thick film coating is one or more of silver, platinum, palladium, palladium oxide, gold and rare earth materials.

Preferably, the covering layer is made from one or more of polyester, polyimide or polyetherimide (PEI), ceramics, silica gel, asbestos, micarex, fabric and fiber.

Preferably, the area of the thick film coating is smaller than or equal to the area of the covering layer or the carrier.

The present invention also provides a use of the thick film element for coating products with substrate heating.

The beneficial effects of the present invention are as follows:

(1) The coated substrate of the thick film element of the present invention has a high heat conductivity, and is suitable for coating products with substrate heating to improve heat transfer efficiency and reduce heat loss when double-sided heating is not required.

(2) The three-layered structure of the thick film element of the present invention could be directly bound by printing or sintering, and the thick film coating would heat the carrier directly without the need of any medium. Hence, heat could be conducted to the carrier directly, thus improving heat conduction efficiency. Additionally, the covering layer of the present invention is overlaid on the thick film coating, avoiding electric leakage of the thick film coating after given electricity and improving safety performance.

The thick film element of the present invention generates heat by the thick film coating, the thickness range of which is at the micrometer level, and has a uniform heat generating rate and long service lifespan.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

The present invention will now be described more specifically with reference to the following embodiments. It is to be noted that the following descriptions of preferred embodiments of this invention are presented herein for purpose of illustration and description only. It is not intended to be exhaustive or to be limited to the precise form disclosed.

The present invention discloses a thick film element having a coated substrate with high heat conductivity, which comprises a carrier, a thick film coating deposited on the carrier and a covering layer overlaid on the coating; the thick film coating is a heating material, and the mode of heating is electrical heating, wherein the carrier, the thick film coating and the covering layer are selected from a material that fulfills every of the following equations:

${{\lambda_{1}A\; \frac{T_{1} - T_{0}}{d_{1}}} = {a \times \lambda_{3}A\; \frac{T_{3} - T_{0}}{d_{3}}}},{{\lambda_{2}A\; \frac{T_{2} - T_{0}}{d_{2}}} = {b \times \lambda_{1}A\; \frac{T_{1} - T_{0}}{d_{1}}}},{{{\lambda_{2}A\; \frac{T_{2} - T_{0}}{d_{2}}} = {c \times \lambda_{3}A\; \frac{T_{3} - T_{0}}{d_{3}}}};}$ 10 ≤ a ≤ 10⁴, 0 < b ≤ 10⁶, 0 < c ≤ 10³;

T₂<T_(Minimum melting point of the covering layer); T₂<T_(Minimum melting point of the carrier);

T₀≤25° C.;

d₂≤50 μm; and d₁≥10 μm; 10 μm≤d₃≤20 cm; T_(Minimum melting point of the carrier)>25° C.; λ₃≥λ₁.

The following embodiments include 20 thick film elements prepared by the inventors, and the materials for preparing the covering layer, the thick film coating and the carrier of the 20 listed thick film elements all satisfy the equations above. The detailed preparing method and formula are provided as follows:

Embodiments

Silver paste with a heat conductivity coefficient of λ₂ is selected to prepare the thick film coating, polyimides with a heat conductivity coefficient of λ₃ is selected to prepare the carrier, and polyimides with a heat conductivity coefficient of λ₁ is selected to prepare the covering layer. The three layers are bound by sintering, The area of the prepared thick film coating is A₂, the thickness is d₂; the area of the covering layer is A₁, the thickness is d₁; the area of the carrier is A₃, the thickness is d₃.

Turn on an external DC power supply to charge the thick film coating. The thick film starts to heat up; when the heating is stabled, measure the surface temperature of the covering layer and the carrier, and the heating temperature of the thick film coating under a stable heating state are measured. Heat transfer rate of the covering layer and the carrier, and heat generating rate of the thick film coating are calculated according to the following formula:

${\lambda_{1}A\; \frac{T_{1} - T_{0}}{d_{1}}},{\lambda_{2}A\; \frac{T_{2} - T_{0}}{d_{2}}},{\lambda_{3}A\; {\frac{T_{3} - T_{0}}{d_{3}}.}}$

Tables 1 to 4 are the 20 thick film elements prepared by the inventors. After provided electricity to heat for 2 minutes, the thick film elements are measured according the national standards to obtain the performance data (heat conductivity coefficient, surface temperature) as shown in the Tables. The thickness, contact area, initial temperature are measured before heating.

The methods to measure the heat conductivity coefficient of the covering layer, the thick film coating and the carrier are as follows:

(1) Switch on the power and adjust the heating voltage to a specific value, then turn on the power switch of the device with 6V power and preheat for 20 minutes;

(2) Conduct zero calibration for the light spot galvanometer;

(3) Calibrate the standard operating voltage of UJ31 potentiometer according to the room temperature, set the commutator switch of the potentiometer to a standard position and adjust the operating current of the potentiometer;

As the voltage of standard batteries varies with the temperature, room temperature calibration is calculated by the following formula:

E _(t) =E ₀−[39.94(t−20)+0.929(t−20)²]; wherein E ₀=1.0186V.

(4) Place a heating plate and lower thermoelectric couples on the bottom part of a thin test specimen; place upper thermoelectric couples on the upper part of the thin test specimen. It should be noted that the thermoelectric couples must be placed at the central position of the test specimen, and cold sections of the thermoelectric couples must be placed in an ice bottle.

(5) Place the commutator switch of the potentiometer is at position 1, measure the initial temperatures at the upper part and the lower part of the test specimen; proceed only when the temperature difference between the upper part and the lower part is smaller than 0.004 mV (0.1° C.).

(6) Pre-add 0.08 mV to the initial thermoelectric potential of the upper thermoelectric couples, turn on the heating switch to start heating; meanwhile, watch the time with a stopwatch; when the light spot of a light spot galvanometer returns to zero position, turn off the heat source to obtain excess temperature and heating time of the upper part.

(7) Measure the thermoelectric potential of the lower thermoelectric couples after 4-5 minutes to obtain excess temperature and heating time of the lower part.

(8) Place the commutator switch of the potentiometer at position 2, turn on the heating switch to measure the heating current.

(9) End the test, turn off the power and clear up the instrument and equipment.

The temperature is measured by using a thermo-couple thermometer as follows:

(1) Connect thermo-sensing wires to the surfaces of the thick film coating, the carrier, and the covering layer of the heating elements, and the outdoor air.

(2) Provide electricity to the heating product with rated power, and measure the temperatures at all parts.

(3) Record the temperature T₀, T₁, T₂, T₃ at all parts of the product at every time interval by a connected computer.

The thickness is measured by using a micrometer and by piling and averaging the values.

The method to measure the melting point is as follows:

The detection instrument: differential scanning calorimeter, model DSC2920, manufactured by TA Instruments (USA). The instrument is qualified (Level A) as verified by Verification Regulation of Thermal Analyzer 014-1996.

(1) Ambient temperature: 20-25° C.; Relative humidity: <80%;

(2) Standard material for instrument calibration: Thermal analysis standard material -Indium; standard melting point 429.7485 K (156.60).

(3) Measuring procedure: referring to “GB/T19466.3-2O04/IS0” for the detection procedure.

Repeat the measurement for three times to ensure normal operation of the instrument before sample testing: weight 1-2 ng of the sample, with an accuracy of 0.01 mg, place the sample in an aluminum sample plate. Testing conditions: heat the sample to 200° C. at a rate of 10° C./min, and repeat the measurement for ten times. Measurement model: collect the information of melting points by the computer and instrument, determine the initial extrapolated temperature of the endothermic melting peak by automatic collection of measured data and program analysis of spectra to directly obtain the measurement model. The measurement results are calculated according to the Bessel formula.

Table 1 is the performance data of the covering layers of the thick film elements in Embodiments 1 to 20. The details are as follows:

TABLE 1 Covering Layer Heat Conductivity Surface Initial Coefficient Thickness d₁ Temperature T_(Minimum melting point of the covering layer) Temperature Heat Transfer λ₁ (W/m · k) (μm) T₁ (° C.) (° C.) T₀ (° C.) Rate/10⁶ Embodiment 1 2.3 4000 50 350 25 0.00023 Embodiment 2 2.2 5000 45 350 25 0.0001584 Embodiment 3 2.3 5000 50 350 25 0.000184 Embodiment 4 4.6 5000 53 350 25 0.0005152 Embodiment 5 2.2 6000 46 350 25 0.0001232 Embodiment 6 2 6000 45 350 25 0.000106667 Embodiment 7 1.8 6000 45 350 25 0.000096 Embodiment 8 2.2 8000 48 350 25 0.000107525 Embodiment 9 2.4 8000 45 350 25 0.000096 Embodiment 1.85 10000 45 350 25 0.0000666 10 Embodiment 2.1 10000 50 350 25 0.000084 11 Embodiment 2.12 20000 50 350 25 0.000053 12 Embodiment 2.2 20000 45 350 25 0.0000352 13 Embodiment 2.23 2000 45 350 25 0.0005798 14 Embodiment 2.2 2000 55 350 25 0.000594 15 Embodiment 2.2 12000 55 350 25 0.000143 16 Embodiment 2.23 12000 45 350 25 5.94667E−05 17 Embodiment 2.05 12000 45 350 25 6.83333E−05 18 Embodiment 2.2 7000 50 350 25 0.000125714 19 Embodiment 2.2 7000 50 350 25 9.42857E−05 20

Table 2 is the performance data of the thick film coatings of the thick film elements in Embodiments 1 to 20. The details are as follows:

TABLE 2 Thick Film Coating Heat Conductivity Heating Initial Coefficient λ₂ Thickness d₂ Temperature Temperature Heat Generating (W/m · k) (μm) Area A₂ (m²) T₂ (° C.) T₀ (° C.) Rate/10⁶ Embodiment 1 380 50 0.016 116 25 11.0656 Embodiment 2 320 50 0.018 110 25 9.792 Embodiment 3 380 40 0.016 103 25 11.856 Embodiment 4 380 40 0.02 112 25 16.53 Embodiment 5 380 30 0.016 98 25 14.79466667 Embodiment 6 381 30 0.016 97 25 14.6304 Embodiment 7 381 30 0.016 95 25 14.224 Embodiment 8 381 25 0.017 108 25 21.50364 Embodiment 9 380 25 0.016 97 25 17.5104 Embodiment 380 25 0.018 100 25 20.52 10 Embodiment 380 30 0.016 100 25 15.2 11 Embodiment 380 30 0.02 108 25 21.02666667 12 Embodiment 381 20 0.016 95 25 21.336 13 Embodiment 381 20 0.026 98 25 36.1569 14 Embodiment 381 30 0.018 99 25 16.9164 15 Embodiment 380.5 30 0.026 110 25 28.03016667 16 Embodiment 380.5 35 0.016 103 25 13.56754286 17 Embodiment 380.5 35 0.02 98 25 15.87228571 18 Embodiment 380.5 25 0.016 94 25 16.80288 19 Embodiment 380.5 25 0.012 102 25 14.06328 20

Table 3 is the performance data of the carriers of the thick film elements in Embodiments 1 to 20. The details are as follows:

TABLE 3 Carrier Heat Conductivity Surface Initial Coefficient Thickness d₃ Temperature T₃ T_(Minimum melting point of the carrier) Temperature Heat Transfer λ₃ (W/m · k) (μm) (° C.) (° C.) T₀ (° C.) Rate/10⁶ Embodiment 1 7.15 20 105 350 25 0.4576 Embodiment 2 7.15 80 100 350 25 0.12065625 Embodiment 3 7.15 50 90 350 25 0.14872 Embodiment 4 7.16 100 108 350 25 0.118856 Embodiment 5 7.16 20 86 350 25 0.349408 Embodiment 6 7.16 200 90 350 25 0.037232 Embodiment 7 7.21 300 84 350 25 0.022687467 Embodiment 8 7.21 80 90 350 25 0.099588125 Embodiment 9 7.21 20 87 350 25 0.357616 Embodiment 7.18 50 95 350 25 0.180936 10 Embodiment 7.18 50 93 350 25 0.1562368 11 Embodiment 7.18 50 105 350 25 0.22976 12 Embodiment 7.15 30 85 350 25 0.2288 13 Embodiment 7.15 30 88 350 25 0.39039 14 Embodiment 7.15 25 85 350 25 0.30888 15 Embodiment 7.17 25 100 350 25 0.55926 16 Embodiment 7.17 50 94 350 25 0.1583136 17 Embodiment 7.22 50 88 350 25 0.181944 18 Embodiment 7.22 50 91 350 25 0.1524864 19 Embodiment 7.22 45 92 350 25 0.128997333 20

Table 4 is the heat transfer rates calculated according to the performance data listed in Tables 1, 2 and 3. The heat transfer rates of the covering layer, the thick film coating and the carrier are calculated by ratio to obtain the limiting condition of the material of the present invention, namely the following equations:

${{\lambda_{3}A\; \frac{T_{3} - T_{0}}{d_{3}}} = {a \times \lambda_{1}A\; \frac{T_{1} - T_{0}}{d_{1}}}},{{\lambda_{2}A\; \frac{T_{2} - T_{0}}{d_{2}}} = {b \times \lambda_{1}A\; \frac{T_{1} - T_{0}}{d_{1}}}},{{{\lambda_{2}A\; \frac{T_{2} - T_{0}}{d_{2}}} = {c \times \lambda_{3}A\; \frac{T_{3} - T_{0}}{d_{3}}}};}$

wherein 10≤a≤10⁴, 0≤b≤10⁶, 0<c≤10³.

TABLE 4 Thick Film Covering Coating Layer Heat Carrier Heat Transfer Generating Heat Transfer Satisfy the Rate Rate Rate a b c Equations? Embodiment 1 230 11065600 457600 1989.5652 48111.304 24.181818 Yes Embodiment 2 158.4 9792000 120656.25 761.71875 61818.182 81.156177 Yes Embodiment 3 184 11856000 148720 808.26087 64434.783 79.72028 Yes Embodiment 4 515.2 16530000 118856 230.69876 32084.627 139.07586 Yes Embodiment 5 123.2 14794666.67 349408 2836.1039 120086.58 42.342095 Yes Embodiment 6 106.6666667 14630400 37232 349.05 137160 392.9523 Yes Embodiment 7 96 14224000 22687.46667 236.32778 148166.67 626.95409 Yes Embodiment 8 107.525 21503640 99588.125 926.18577 199987.35 215.92574 Yes Embodiment 9 96 17510400 357616 3725.1667 182400 48.964252 Yes Embodiment 10 66.6 20520000 180936 2716.7568 308108.11 113.41027 Yes Embodiment 11 84 15200000 156236.8 1859.9619 180952.38 97.288219 Yes Embodiment 12 53 21026666.67 229760 4335.0943 396729.56 91.515785 Yes Embodiment 13 35.2 21336000 228800 6500 606136.36 93.251748 Yes Embodiment 14 579.8 36156900 390390 673.31839 62360.987 92.617383 Yes Embodiment 15 594 16916400 308880 520 28478.788 54.7669 Yes Embodiment 16 143 28030166.67 559260 3910.9091 196015.15 50.120099 Yes Embodiment 17 59.46666667 13567542.86 158313.6 2662.2242 228153.75 85.700425 Yes Embodiment 18 68.33333333 15872285.71 181944 2662.5951 232277.35 87.237203 Yes Embodiment 19 125.7142857 16802880 152486.4 1212.96 133659.27 110.19265 Yes Embodiment 20 94.28571429 14063280 128997.3333 1368.1535 149156 109.01993 Yes The results listed in Table 4 show that the thick films prepared according to Embodiments 1 to 20 all satisfy the equations; and the carrier, i.e. coated substrate, has the function of generating heat and the temperature difference between the two sides are more than 40° C., so as to achieve the function of heat generation. When in use, the product could reduce heat loss when the coated substrate of the thick film element is heated, and the temperature could rise to more than 100° C. after giving electricity for two minutes, which demonstrates that the thick film element of the present invention has high heat generation efficiency.

Tables 5 to 8 are the performance data of the thick film elements in contrasting examples 1 to 10 of the present invention. All the performance data is measured as those shown in Tables 1 to 4. The details are as follows:

TABLE 5 Covering Layer Heat Conductivity Surface Initial Coefficient λ₁ Thickness d₁ Temperature T_(Minimum melting point of the covering layer) Temperature Heat Transfer Rate/ (W/m · k) (μm) T₁ (° C.) (° C.) T₀ (° C.) 10⁶ Contrasting 7.18 25 113 350 25 0.4043776 Example 1 Contrasting 2.2 25 55 350 25 0.14784 Example 2 Contrasting 2.23 25 102 350 25 0.1098944 Example 3 Contrasting 7.17 50 53 350 25 0.2248512 Example 4 Contrasting 7.21 50 97 350 25 0.1661184 Example 5 Contrasting 7.18 75 51 350 25 0.139387733 Example 6 Contrasting 1.8 75 94 350 25 0.026496 Example 7 Contrasting 2.2 75 47 350 25 0.036138667 Example 8 Contrasting 2.4 100 93 350 25 0.026112 Example 9 Contrasting 7.18 100 44 350 25 0.0763952 Example 10

TABLE 6 Thick Film Coating Heat Conductivity Heating Initial Coefficient λ₂ Thickness d₂ Temperature Temperature Heat Generating (W/m · k) (μm) Area A₂ (m²) T₂ (° C.) T₀ (° C.) Rate/10⁶ Contrasting 382 50 0.016 116 25 11.12384 Example 1 Contrasting 382 50 0.056 56 25 13.26304 Example 2 Contrasting 382 40 0.016 103 25 11.9184 Example 3 Contrasting 382 40 0.056 55 25 16.044 Example 4 Contrasting 382 30 0.016 98 25 14.87253333 Example 5 Contrasting 382 30 0.056 52 25 19.2528 Example 6 Contrasting 382 30 0.016 95 25 14.26133333 Example 7 Contrasting 382 25 0.056 49 25 20.53632 Example 8 Contrasting 382 25 0.016 97 25 17.60256 Example 9 Contrasting 382 25 0.056 46 25 17.96928 Example 10

TABLE 7 Carrier Heat Conductivity Surface Initial Coefficient Thickness d₃ Temperature T_(Minimum melting point of the carrier) Temperature Heat Transfer λ₃ (W/m · k) (mm) T₃ (° C.) (° C.) T₀ (° C.) Rate/10³ Contrasting 7.16 1 105 350 25 9.1648 Example 1 Contrasting 7.16 2 42 350 25 3.40816 Example 2 Contrasting 7.16 4 87 350 25 1.77568 Example 3 Contrasting 7.18 1 43 350 25 7.23744 Example 4 Contrasting 7.18 2 86 350 25 3.50384 Example 5 Contrasting 7.18 1 40 350 25 6.0312 Example 6 Contrasting 7.21 2 84 350 25 3.40312 Example 7 Contrasting 7.21 3 38 350 25 1.749626667 Example 8 Contrasting 7.22 1 87 350 25 7.16224 Example 9 Contrasting 7.22 2 40 350 25 3.0324 Example 10

TABLE 8 Thick Film Covering Coating Layer Heat Carrier Heat Transfer Generating Heat Transfer Satisfy the Rate Rate Rate a b c equations? Contrasting 404377.6 11123840 9164.8 0.022664 27.508546 1213.757 No Example 1 Contrasting 147840 13263040 3408.16 0.023053 89.712121 3891.5544 No Example 2 Contrasting 109894.4 11918400 1775.68 0.0161581 108.45321 6712.0202 No Example 3 Contrasting 224851.2 16044000 7237.44 0.0321877 71.353855 2216.8059 No Example 4 Contrasting 166118.4 14872533.33 3503.84 0.0210924 89.529717 4244.6383 No Example 5 Contrasting 139387.7333 19252800 6031.2 0.0432692 138.12406 3192.2006 No Example 6 Contrasting 26496 14261333.33 3403.12 0.128439 538.24477 4190.6643 No Example 7 Contrasting 36138.66667 20536320 1749.626667 0.0484143 568.26446 11737.544 No Example 8 Contrasting 26112 17602560 7162.24 0.2742892 674.11765 2457.6892 No Example 9 Contrasting 76395.2 17969280 3032.4 0.0396936 235.21478 5925.7618 No Example 10

Material and structure of the thick film elements in the Contrasting Examples 1 to 10 listed in the above tables neither meet the material selection requirement of the present invention, nor satisfy the equations of the present invention. After given electricity and heat generation, the temperature differences between the two sides of the thick film elements in the Contrasting Examples 1 to 10 are not significantly different, and the heating temperature difference between the covering layer and the carrier is smaller than 15° C. The thick film elements prepared according to such material selections do not meet the requirement of the thick film element having a coated substrate with high heat conductivity of the present invention or meet the product requirement of the present invention, which demonstrates the heat transfer rate and correlation of the present invention.

According to the disclosure and teaching of above-mentioned specification, those skilled in the art of the present invention can still make changes and modifications to above-mentioned embodiment, therefore, the scope of the present invention is not limited to the specific embodiments disclosed and described above, and all those modifications and changes to the present invention are within the scope of the present invention as defined in the appended claims. Besides, although some specific terminologies are used in the specification, it is merely as a clarifying example and shall not be constructed as limiting the scope of the present invention in any way. 

1. A thick film element having a coated substrate with high heat conductivity, comprising: a carrier; a thick film coating deposited on the carrier; and a covering layer overlaid on the coating, wherein the thick film coating is a heating material, and a mode of heating is electrical heating, wherein the carrier, the thick film coating and the covering layer are selected from a material that fulfills every of following equations: ${{\lambda_{3}A\; \frac{T_{3} - T_{0}}{d_{3}}} = {a \times \lambda_{1}A\; \frac{T_{1} - T_{0}}{d_{1}}}},{{\lambda_{2}A\; \frac{T_{2} - T_{0}}{d_{2}}} = {b \times \lambda_{1}A\; \frac{T_{1} - T_{0}}{d_{1}}}},{{{\lambda_{2}A\; \frac{T_{2} - T_{0}}{d_{2}}} = {c \times \lambda_{3}A\; \frac{T_{3} - T_{0}}{d_{3}}}};}$ wherein 10≤a≤10⁴, 0≤b≤10⁶, 0<c≤10³; T₂<T_(Minimum melting point of the covering layer); T₂<T_(Minimum melting point of the carrier); T₀<25° C.; wherein a value of $\lambda_{1}A\; \frac{T_{1} - T_{0}}{d_{1}}$ represents a heat transfer rate of the covering layer; a value of $\lambda_{2}A\; \frac{T_{2} - T_{0}}{d_{2}}$ represents a heat generating rate of the thick film coating; a value of $\lambda_{3}A\; \frac{T_{3} - T_{0}}{d_{3}}$ represents a neat transfer rate of the carrier; λ₁ represents a heat conductivity coefficient of the covering layer at a temperature of T₁; λ₂ represents a heat conductivity coefficient of the thick film coating at a temperature of T₂; λ₃ represents a heat conductivity coefficient of the carrier at a temperature of T₃; A represents a contact area of the thick film coating with the covering layer or the carrier; d₁ represents a thickness of the covering layer; d₂ represents a thickness of the thick film coating; d₃ represents a thickness of the carrier; T₀ represents an initial temperature of the thick film element; T₁ represents a surface temperature of the covering layer; T₂ represents a heating temperature of the thick film coating; T₃ represents a surface temperature of the carrier; wherein d₂≤50 μm; d₁≥10 μm; 10 μm≤d₃≤20 cm; T_(Minimum melting point of the carrier)>25° C.; and λ₃≥λ₁.
 2. The thick film element according to claim 1, wherein the heat conductivity coefficient λ₃ of the carrier is higher than or equal to 3 W/m·k, the heat conductivity coefficient λ₁ of the covering layer is smaller than or equal to 3 W/m·k; and 10≤a≤10⁴, 10⁴≤b≤10⁶, 10≤c≤10³.
 3. The thick film element according to claim 2, wherein an area between the carrier and the covering layer not having the thick film coating is bound by printing or sintering.
 4. The thick film element according to claim 1, wherein the carrier and the thick film coating are bound by printing coating, spraying or sintering, and the thick film coating and the covering layer are bound by printing, sintering, or gluing.
 5. The thick film element according to claim 1, wherein the carrier comprises polyimides, organic insulating materials, inorganic insulating materials, ceramics, glass ceramics, quartz, stone materials, fabrics and fibers.
 6. The thick film element according to claim 1, wherein the thick film coating is one or more of silver, platinum, palladium, palladium oxide, gold and rare earth materials.
 7. The thick film element according to claim 1, wherein the covering layer is made from one or more of polyester, polyimide or polyetherimide (PEI), ceramics, silica gel, asbestos, micarex, fabric and fiber.
 8. The thick film element according to claim 1, wherein an area of the thick film coating is smaller than or equal to an area of the covering layer or an area of the carrier.
 9. An use of a thick film element, for coating products having a single-sided heating substrate, wherein the thick film element has a coated substrate with high heat conductivity and comprises: a carrier: a thick film coating deposited on the carrier; and a covering layer overlaid on the coating, wherein the thick film coating is a heating material, and a mode of heating is electrical heating, wherein the carrier, the thick film coating and the covering layer are selected from a material that fulfills every of following equations: ${{\lambda_{3}A\; \frac{T_{3} - T_{0}}{d_{3}}} = {a \times \lambda_{1}A\; \frac{T_{1} - T_{0}}{d_{1}}}},{{\lambda_{2}A\; \frac{T_{2} - T_{0}}{d_{2}}} = {b \times \lambda_{1}A\; \frac{T_{1} - T_{0}}{d_{1}}}},{{{\lambda_{2}A\; \frac{T_{2} - T_{0}}{d_{2}}} = {c \times \lambda_{3}A\; \frac{T_{3} - T_{0}}{d_{3}}}};}$ wherein 10≤a≤10⁴, 0<b≤10⁶, 0<c≤0; T₂<T_(Minimum melting point of the covering layer); T₂<T_(Minimum melting point of the carrier); T₀≤25° C.; wherein a value of $\lambda_{1}A\; \frac{T_{1} - T_{0}}{d_{1}}$ represents a heat transfer rate of the covering layer; a value of $\lambda_{2}A\; \frac{T_{2} - T_{0}}{d_{2}}$ represents a neat generating rate of the thick film coating: a value of $\lambda_{3}A\; \frac{T_{3} - T_{0}}{d_{3}}$ represents a neat transfer rate of the carrier: λ₁ represents a heat conductivity coefficient of the covering layer at a temperature of T₁; λ₂ represents a heat conductivity coefficient of the thick film coating at a temperature of T₂; λ₃ represents a heat conductivity coefficient of the carrier at a temperature of T₃; A represents a contact area of the thick film coating with the covering layer or the carrier; d₁ represents a thickness of the covering layer; d₂ represents a thickness of the thick film coating; d₃ represents a thickness of the carrier; T₀ represents an initial temperature of the thick film element; T₁ represents a surface temperature of the covering layer; T₂ represents a heating temperature of the thick film coating; T₃ represents a surface temperature of the carrier; wherein d₂≤50 μm; d₁≥10 μm; 10 μm≤d₃≤20 cm; T_(Minimum melting point of the carrier)>25° C.; and λ₃≥λ₁.
 10. The use of the thick film element according to claim 9, wherein the heat conductivity coefficient λ₃ of the carrier is higher than or equal to 3 W/m·k, the heat conductivity coefficient λ₁ of the covering layer is smaller than or equal to 3 W/m·k; and 10≤a≤10⁴, 10⁴≤b≤10⁶, 10≤c≤10³.
 11. The use of the thick film element according to claim 10, wherein an area between the carrier and the covering layer not having the thick film coating is bound by printing or sintering.
 12. The use of the thick film element according to claim 9, wherein the carrier and the thick film coating are bound by printing coating, spraying or sintering, and the thick film coating and the covering layer are bound by printing, sintering, or gluing.
 13. The use of the thick film element according to claim 9, wherein the carrier comprises polyimides, organic insulating materials, inorganic insulating materials, ceramics, glass ceramics, quartz, stone materials, fabrics and fibers.
 14. The use of the thick film element according to claim 9, wherein the thick film coating is one or more of silver, platinum, palladium, palladium oxide, gold and rare earth materials.
 15. The use of the thick film element according to claim 9, wherein the covering layer is made from one or more of polyester, polyimide or polyetherimide (PEI), ceramics, silica gel, asbestos, micarex, fabric and fiber.
 16. The use of the thick film element according to claim 9, wherein an area of the thick film coating is smaller than or equal to an area of the covering layer or an area of the carrier. 